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This book derives and evaluates fast expressions for calculating pressures generated by planar pistons and potentials generated by volume sources, which are called the fast near-field method (FNM). The FNM expressions are compared with several existing methods such as the impulse response method, the Field II program, the Rayleigh-Sommerfeld integrals and the singularity cancellation method. Comparison results show that the FNM expressions achieve smaller errors in less time (or less sample points).